David Bowie spent much of his final year on this planet working on a musical, Lazarus, based on his 1976 sci-fi movie The Man Who Fell to Earth. Written with Irish playwright Enda Walsh (Once), it seemed like a curious use of his time – but as we know now, it was part of his elaborate farewell gesture. Lazarus worked poignantly onstage – especially the climactic scene where alien Michael C. Hall (from Dexter) and his angel daughter swim like dolphins through puddles of milk while singing "Heroes," before he blasts off in his rocket back to his home planet.

The Lazarus soundtrack has the title song, already familiar from his still-astounding Blackstar, along with three new Bowie songs. The other 18 tracks are theater pros doing his hits ("Changes," "All The Young Dudes") or deep cuts ("It's No Game," "Always Crashing in the Same Car"), recorded the day after his death. The songs have already been defined by the master – if you've heard Bowie sing "Life on Mars," not to mention Barbara Streisand or Lorde, you probably won't play this version twice. But the cast sometimes brings fresh nuance – especially "Absolute Beginners," where Hall and Cristin Milioti revive a long-forgotten Eighties movie theme as a doo-wop wedding hymn.

The real attraction is the three new Bowie tracks, recorded during the Blackstar sessions with the same great jazzy band and producer Tony Visconti. While he intended them for the musical, not his album, they're a chilling last transmission. Bowie comes on violent and threatening in the industrial "Killing a Little Time," snarling, "I've got a handful of songs to sing/To sting your soul, to fuck you over." "When I Met You" is pop charm, with a Lindsey Buckingham quiver in the guitar twang. But the real prize is "No Plan," where Bowie croons an eerie torch song about drifting into space, floating over New York City – "There's no music here/I'm lost in streams of sound." It's a crucial part of Bowie's long goodbye to a world that wasn't quite ready to let go of him.